RepTiles v.2.0.1 (screenshot) is a plane tiling shareware written by two mathematicians Daniel H Huson and
http://www-ab.informatik.uni-tuebingen.de/people/delgado/welcome.html.
The program is capable of generating all possible periodic tiling of the plane. By the words of the authors: “… for interactively designing and systematically generating periodic 2-dimensional tilings and patterns, study symmetry and 2-dimensional geometry, if you are a mathematician, enumerate possible 2-dimensional crystal-structures, if you are a crystallographer or chemist, design complex and interesting patterns, if you are a designer, or explore a whole new world of fascinating periodic structures, if you are, well, just interested.” This program is a bit mathematical, but can be fun for layperson. It is a rare tool for crystallographer and mathematicians. URL: ftp://ftp.uni-bielefeld.de/pub/math/tiling/reptiles/.
(Note: This program is from 1995 era. The software downloaded from the ftp site is missing data files, making the software not usable. I don't have a copy of it.)
Mac

Some other programs for polytopes

HyperDimension1999 Ishihama Yoshiaki has written several interesting programs. Many of them are related to high dimensions, including a 4 and 5 dimensional Rubic cube simulators. His programs are small and original, but the interface is very crude. Check out his webpage for more Source www.asahi-net.or.jp. Ishihama Yoshiaki's software are usually raw and unpolished. (2002-07)
MacJava

HyperSpace 2.0 (1990) is another higher-dimensional polytope viewer, by Paul Bruke. It does not let you drag and spin, but offers both multiple slice view and projection view on about 4 regular polyhedrons. Paul Bruke's software page is at:
Source local.wasp.uwa.edu.au. Ask Paul to update this software. (2002)
Mac

Stewart Coffin's The Puzzling World of Polyhedral Dissections, now online free at:
Source johnrausch.com
This book specify in detail a whole type of puzzles that is made of interlocking
blocks of various shapes that assemble into regular polyhedrons or beautiful objects of such symmetry.